Alvin has a prism-like water tank whose base area is $0.9$ square meters and height is $0.6$ meters. He wants to buy guppy fish, and the pet store owner tells him to make sure their density in the tank isn't more than $5$ fish per cubic meter. How many fish can Alvin get, at most?
Explanation: This is a density word problem. To solve it, we can use the following equation, which is the volume definition of density: ${\text{Density}}=\dfrac{{\text{Total quantity}}}{{\text{Volume}}}$ What do we know? The base area of the prism-like tank is $0.9$ square meters and its height is $0.6$ meters (we can use this to find the ${\text{volume}}$ ). The ${\text{density}}$ of the fish shouldn't be more than $ 5$ fish per cubic meter. What do we need to find? The maximum possible number of fish, which is the ${\text{total quantity}}$ We want the ${\text{density}}$ to be ${5}$ fish per cubic meter at most. So this is the inequality we want to solve: $\begin{aligned} {\text{Density}} &\leq {5}\\\\ \dfrac{{\text{Total quantity}}}{{\text{Volume}}} &\leq {5} \end{aligned}$ If Alvin fills the whole tank, the ${\text{volume}}$ of the water is $0.9\cdot 0.6={0.54}$ cubic meters. Let's denote the number of fish as $ n$. Now we can plug ${\text{total quantity}=n}$ and ${\text{volume}=0.54}$ in the inequality. $\begin{aligned} \dfrac{{\text{Total quantity}}}{{\text{Volume}}} &\leq {5} \\\\ \dfrac{{n}}{{0.54}} &\leq {5} \\\\ \cancel{0.54}\cdot\dfrac{ n}{\cancel{0.54}} &\leq 0.54\cdot 5 \\\\ n& \leq 2.7 \end{aligned}$ The number of fish must be less than $2.7$. If there are more fish, the density will be more than $5$, which is too high. Also, the number of fish must be a whole number. Therefore, at most, Alvin can have $2$ fish.